There are no rules about how to do mazes. I have always drawn the mazes in the books I have transcribed (and our agency has always drawn them).
Your suggestion about using a full cell for the dark parts of the maze is interesting, but I think this one is too big to fit across one braille page (I think - but maybe not?) that way and then you would have to deal with facing pages...which defeats the purpose. You would have to come up with a really good transcriber's note to explain what you have done.
So my first answer is: draw it. But if you can get it on one page using braille dots and can write a TN that adequately explains what you have done, you can try it. If you have the ability to emboss it that would be best...you can then get a really good feel for whether or not the paths are easily followed by touch and that should be the deciding factor on whether or not braille dots would work for this maze.